{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"name":"gp_homo_hetero.ipynb","version":"0.3.2","provenance":[],"collapsed_sections":[]},"kernelspec":{"name":"python3","display_name":"Python 3"}},"cells":[{"metadata":{"id":"xAYPKSFrG8AF","colab_type":"code","outputId":"8907acd2-e115-4677-b42d-e4f8c4e48072","executionInfo":{"status":"ok","timestamp":1554370193284,"user_tz":420,"elapsed":43787,"user":{"displayName":"Stratis Markou","photoUrl":"","userId":"09754366312766083286"}},"colab":{"base_uri":"https://localhost:8080/","height":343}},"cell_type":"code","source":["#!pip3 install http://download.pytorch.org/whl/cu92/torch-0.4.1-cp36-cp36m-linux_x86_64.whl\n","#!pip3 install torchvision\n","! pip install GPy\n","import GPy\n","import time\n","import copy\n","import math\n","import matplotlib.pyplot as plt\n","import numpy as np\n","\n","from google.colab import files\n","%config InlineBackend.figure_format = 'svg'"],"execution_count":2,"outputs":[{"output_type":"stream","text":["Collecting GPy\n","\u001b[?25l  Downloading https://files.pythonhosted.org/packages/98/7d/e55ffc3b16b68e8b50ccecacec56715bcf49d5c2f204f5ba60374d419611/GPy-1.9.6.tar.gz (873kB)\n","\u001b[K    100% |████████████████████████████████| 880kB 20.9MB/s \n","\u001b[?25hRequirement already satisfied: numpy>=1.7 in /usr/local/lib/python3.6/dist-packages (from GPy) (1.14.6)\n","Requirement already satisfied: scipy>=0.16 in /usr/local/lib/python3.6/dist-packages (from GPy) (1.1.0)\n","Requirement already satisfied: six in /usr/local/lib/python3.6/dist-packages (from GPy) (1.11.0)\n","Collecting paramz>=0.9.0 (from GPy)\n","\u001b[?25l  Downloading https://files.pythonhosted.org/packages/fd/78/b0f0164a32518bfd3b98cb2e149b7a4d5504d13fb503b31a6c59b958ed18/paramz-0.9.4.tar.gz (70kB)\n","\u001b[K    100% |████████████████████████████████| 71kB 23.4MB/s \n","\u001b[?25hRequirement already satisfied: decorator>=4.0.10 in /usr/local/lib/python3.6/dist-packages (from paramz>=0.9.0->GPy) (4.4.0)\n","Building wheels for collected packages: GPy, paramz\n","  Building wheel for GPy (setup.py) ... \u001b[?25ldone\n","\u001b[?25h  Stored in directory: /root/.cache/pip/wheels/97/82/1d/32a361e1ff2b4d9129a60343831dd99cdc74440e2db1c55264\n","  Building wheel for paramz (setup.py) ... \u001b[?25ldone\n","\u001b[?25h  Stored in directory: /root/.cache/pip/wheels/a9/fc/74/3bbd263c43ed98d67343df24cebf0a0ee34afee40d769fda9c\n","Successfully built GPy paramz\n","Installing collected packages: paramz, GPy\n","Successfully installed GPy-1.9.6 paramz-0.9.4\n"],"name":"stdout"}]},{"metadata":{"id":"ym6HBK-s8GnO","colab_type":"code","outputId":"dc881fab-e833-40f5-81cb-9d966b3c2e77","executionInfo":{"status":"ok","timestamp":1554370971551,"user_tz":420,"elapsed":4492,"user":{"displayName":"Stratis Markou","photoUrl":"","userId":"09754366312766083286"}},"colab":{"base_uri":"https://localhost:8080/","height":618}},"cell_type":"code","source":["np.random.seed(2)\n","no_points = 400\n","lengthscale = 1\n","variance = 1.0\n","sig_noise = 0.3\n","x = np.random.uniform(-3, 3, no_points)[:, None]\n","x.sort(axis = 0)\n","\n","\n","k = GPy.kern.RBF(input_dim = 1, variance = variance, lengthscale = lengthscale)\n","C = k.K(x, x) + np.eye(no_points)*sig_noise**2\n","\n","y = np.random.multivariate_normal(np.zeros((no_points)), C)[:, None]\n","y = (y - y.mean())\n","x_train = x[75:325]\n","y_train = y[75:325]\n","\n","rbf = GPy.kern.RBF(input_dim=1, variance=1, lengthscale=1.)\n","#rbf = GPy.kern.MLP(input_dim=1, variance=1.0, weight_variance=1.0, bias_variance=1.0)\n","white = GPy.kern.White(input_dim=1, variance = 0.09)\n","m = GPy.models.GPRegression(x_train, y_train, rbf + white)\n","\n","#m.optimize_restarts(num_restarts = 3)\n","print(m.parameters[0])\n","\n","means, total_unc = m.predict(np.linspace(-5, 5, 200)[:, None])\n","means = means.reshape(-1)\n","\n","aleatoric = m.parameters[0].white.parameters[0][0]**0.5\n","total_unc = (total_unc/2).reshape(-1)**0.5\n","epistemic = (total_unc**2 - aleatoric**2)**0.5\n","\n","\n","c = ['#1f77b4', '#ff7f0e', '#2ca02c', '#d62728', '#9467bd',\n","     '#8c564b', '#e377c2', '#7f7f7f', '#bcbd22', '#17becf']\n","\n","plt.figure(figsize = (6, 5))\n","plt.style.use('default')\n","plt.scatter(x_train, y_train, s = 10, marker = 'x', color = 'black', alpha = 0.5)\n","plt.fill_between(np.linspace(-5, 5, 200), means + aleatoric, means + total_unc, color = c[0], alpha = 0.3, label = 'Epistemic + Aleatoric')\n","plt.fill_between(np.linspace(-5, 5, 200), means - total_unc, means - aleatoric, color = c[0], alpha = 0.3)\n","plt.fill_between(np.linspace(-5, 5, 200), means - aleatoric, means + aleatoric, color = c[1], alpha = 0.4, label = 'Aleatoric')\n","plt.plot(np.linspace(-5, 5, 200), means, color = 'black', linewidth = 1)\n","plt.xlim([-5, 5])\n","plt.ylim([-5, 7])\n","plt.xlabel('$x$', fontsize=30)\n","plt.title('GP Ground truth', fontsize=40)\n","plt.tick_params(labelsize=30)\n","plt.xticks(np.arange(-4, 5, 2))\n","plt.yticks(np.arange(-4, 7, 2))\n","plt.gca().set_yticklabels([])\n","plt.gca().yaxis.grid(alpha=0.3)\n","plt.gca().xaxis.grid(alpha=0.3)\n","plt.savefig('gp_homo.pdf', bbox_inches = 'tight')\n","\n","files.download(\"gp_homo.pdf\")\n","\n","plt.show()"],"execution_count":4,"outputs":[{"output_type":"stream","text":["  \u001b[1msum.           \u001b[0;0m  |  value  |  constraints  |  priors\n","  \u001b[1mrbf.variance   \u001b[0;0m  |    1.0  |      +ve      |        \n","  \u001b[1mrbf.lengthscale\u001b[0;0m  |    1.0  |      +ve      |        \n","  \u001b[1mwhite.variance \u001b[0;0m  |   0.09  |      +ve      |        \n"],"name":"stdout"},{"output_type":"display_data","data":{"text/plain":["<Figure size 600x500 with 1 Axes>"],"image/svg+xml":"<?xml version=\"1.0\" encoding=\"utf-8\" 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np.eye(no_points)*(x+2)**2*sig_noise**2\n","\n","y = np.random.multivariate_normal(np.zeros((no_points)), C)[:, None]\n","y = (y - y.mean())\n","x_train = x[75:325]\n","y_train = y[75:325]\n","\n","rbf = GPy.kern.RBF(input_dim=1, variance=1, lengthscale=1.)\n","\n","mean = []\n","var = []\n","no_points = len(x_train)\n","all_x = np.linspace(-10, 10, 150)\n","for x in all_x:\n","    xs = np.array([[x] + list(x_train)]).T\n","    C = k.K(xs, xs)\n","    \n","    data_var = np.eye(no_points)*(xs[1:]-2)**2*sig_noise**2\n","    pred_var = np.eye(1)*(xs[:1]+2)**2*sig_noise**2\n","    \n","    mean.append(C[:1, 1:].dot(np.linalg.inv(C[1:, 1:] + data_var)).dot(y_train))\n","    var.append(C[:1, :1] + pred_var - C[:1, 1:].dot(np.linalg.inv(C[1:, 1:] + data_var)).dot(C[:1, 1:].T))\n","\n","means = np.array(mean)[:, 0, 0]\n","var = np.array(var)[:, 0, 0]\n","\n","aleatoric = abs(all_x+2)*sig_noise\n","total_unc = var**0.5\n","epistemic = (total_unc**2 - aleatoric**2)**0.5\n","\n","\n","c = ['#1f77b4', '#ff7f0e', '#2ca02c', '#d62728', '#9467bd',\n","     '#8c564b', '#e377c2', '#7f7f7f', '#bcbd22', '#17becf']\n","\n","plt.figure(figsize = (6, 5))\n","plt.style.use('default')\n","plt.scatter(x_train, y_train, s = 10, marker = 'x', color = 'black', alpha = 0.5)\n","plt.fill_between(all_x, means + aleatoric, means + total_unc, color = c[0], alpha = 0.3, label = 'Epistemic + Aleatoric')\n","plt.fill_between(all_x, means - total_unc, means - aleatoric, color = c[0], alpha = 0.3)\n","plt.fill_between(all_x, means - aleatoric, means + aleatoric, color = c[1], alpha = 0.4, label = 'Aleatoric')\n","plt.plot(all_x, means, color = 'black', linewidth = 1)\n","plt.xlim([-5, 5])\n","plt.ylim([-5, 7])\n","plt.xlabel('$x$', fontsize=30)\n","plt.title('GP Ground truth', fontsize=40)\n","plt.tick_params(labelsize=30)\n","plt.xticks(np.arange(-4, 5, 2))\n","plt.yticks(np.arange(-4, 7, 2))\n","plt.gca().set_yticklabels([])\n","plt.gca().yaxis.grid(alpha=0.3)\n","plt.gca().xaxis.grid(alpha=0.3)\n","plt.savefig('gp_hetero.pdf', bbox_inches = 'tight')\n","\n","#files.download(\"gp_hetero.pdf\")\n","\n","plt.show()"],"execution_count":0,"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 600x500 with 1 Axes>"],"image/svg+xml":"<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Created with matplotlib (https://matplotlib.org/) -->\n<svg height=\"397.0625pt\" version=\"1.1\" viewBox=\"0 0 356.2 397.0625\" width=\"356.2pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n <defs>\n  <style type=\"text/css\">\n*{stroke-linecap:butt;stroke-linejoin:round;}\n  </style>\n </defs>\n <g id=\"figure_1\">\n  <g id=\"patch_1\">\n   <path d=\"M 0 397.0625 \nL 356.2 397.0625 \nL 356.2 0 \nL 0 0 \nz\n\" 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